Wavelet Based Damage Detection Approach for Bridge ... · Wavelet Based Damage Detection Approach for Bridge Structures Utilising Vehicle Vibration Patrick J. McGetrick1 and Chul
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Wavelet Based Damage Detection Approach for BridgeStructures Utilising Vehicle Vibration
McGetrick, P. J., & Kim, C. W. (2012). Wavelet Based Damage Detection Approach for Bridge StructuresUtilising Vehicle Vibration. In Proceedings of 9th German Japanese Bridge Symposium, GJBS09. [38]
Published in:Proceedings of 9th German Japanese Bridge Symposium, GJBS09
Document Version:Peer reviewed version
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Over the past two decades there has been a focus on the development of effective techniques for the monitoring of the
condition of structures such as bridges. These structural health monitoring (SHM) techniques [1-3], the majority of which
are vibration based, generally require measurement gauges and data acquisition electronics to be installed directly on the
bridge, which can be difficult and time consuming. However, they can be effective in providing a warning to public if a
bridge’s condition deteriorates and it becomes unsafe. Due to the ageing of existing bridge stocks worldwide, these
approaches are arguably becoming a more critical part of bridge management systems and maintenance strategies. More
recently, there has been a move towards the development of indirect vibration-based approaches utilising the response of
a vehicle passing over a bridge. This type of approach aims to reduce or eliminate the need for direct instrumentation of
the bridge thus providing a more efficient and low-cost alternative.
This paper investigates such an approach; an alternative wavelet-based approach for the periodic monitoring of bridge
structures which consists of the use of a vehicle fitted with accelerometers on its axles. The aim of the approach is to
utilise the vehicle response to detect changes in the bridge response which correspond to variations in the structural
condition, i.e., damage. In this paper, the effectiveness of this approach is investigated both theoretically and
experimentally.
To date, the use of this type of indirect approach to identify bridge properties has been investigated by many
researchers. The feasibility of extracting the natural frequency of a bridge from the acceleration response of a passing
vehicle has been verified theoretically [4-7]. Yang et al. [4] use a tractor-trailer system in simulations; the tractor serves as
the exciter of the bridge while the trailer acts as the receiver of the bridge vibration. The bridge frequency is extracted
from the spectra of the vehicle accelerations. In addition, they find that the magnitude of the peak response in the vehicle
acceleration spectra increases with vehicle speed but decreases with increasing bridge damping ratio. McGetrick et al. [6]
identify both the frequency and changes in damping of the bridge from vehicle accelerations and note that it is difficult to
detect both of these parameters in the presence of a rough road profile. Yang et al. [4] and González et al. [7] both
highlight that frequency matching between the vehicle and the bridge is beneficial for frequency detection. Yang and
Chang [8] present a parametric study which indicates some of the best conditions for frequency detection using this type
of indirect approach.
Field trials have taken place to investigate a drive-by inspection method for bridges [9-12]. It is found that accurate
determination of the bridge natural frequency is feasible for low speeds and when there is sufficiently high dynamic
excitation of the bridge. This is due to the road roughness having a greater influence than bridge vibration on the vehicle
response. The empirical mode decomposition technique is used by Yang and Chang [12] to extract frequencies of higher
modes from the vehicle response. Experimental investigations have also been conducted to examine the feasibility of such
an approach as part of a drive-by inspection system for bridge monitoring. In a laboratory experiment, Toshinami et al.
[13] extract the bridge frequency from the dynamic response of a vehicle. Kim and Kawatani [14] investigate a condition
screening and damage detection approach which utilises an inspection car, acting as an actuator to the bridge, for data
acquisition from wireless sensor nodes installed on the bridge. It is found that the damage location and severity is
identified by the approach via analysis and comparison of the stiffness distribution throughout the bridge between intact
and damaged states.
Bu et al. [15] also present a numerical investigation of a bridge condition assessment technique which utilises the
dynamic response of a vehicle moving along a beam to detect damage in terms of stiffness reduction. They find that
vehicle speed, measurement noise, road surface roughness and model errors do not have a significant effect on the
accuracy of the approach. González et al. [16] also present a novel algorithm which, using the vehicle accelerations as the
input, identifies the damping of a bridge. It is found that the algorithm can also be used to identify the bridge stiffness and
is not very sensitive to low levels of signal noise, the road roughness or errors in the assumed numerical models.
The popularity of wavelet theory and in particular, the use of wavelets in techniques to identify structural damage, has
risen considerably in recent years as it allows a signal to be analysed in both time and frequency domains simultaneously.
Hester and González [17] provide examples demonstrating the capacity of the wavelet transform to capture
time-frequency information while Reda Taha et al. [18] discuss the use of wavelet analysis in structural health monitoring
applications. Their use has also been extended to indirect approaches for the purpose of damage detection.
Nguyen and Tran [19] present a wavelet based approach to identify cracks in a bridge from the vehicle response.
Numerical simulations are carried out using a cracked finite element (FE) beam model and a 4 degree-of-freedom half-car
vehicle model however no road profile is included. The aim is to determine the existence and location of cracks in the
beam from the vehicle displacement response using the Symlet wavelet transform. A two-crack scenario is investigated
varying vehicle speed and crack depth is also varied as a percentage of the beam depth. Peaks at particular scales are
observed in the wavelet transform of the vehicle displacement response when it passes over cracks while crack depths of
up to 10% are detected. It is found that deeper cracks are easier to detect while higher speeds provide poorer detection
ability. The effect of white noise on crack detection is investigated and for 6% noise, a 50% crack depth is detected at 2
m/s. Experimental testing is recommended by the authors.
Khorram et al. [20] also carry out a numerical investigation in which a very simple vehicle-bridge interaction (VBI)
model is used to compare two methods which utilise a wavelet transform to identify the existence and location of cracks in
beams; a “fixed sensor approach” and a “moving sensor approach”, which are direct and indirect methods respectively.
Using the Gaussian 4 mother wavelet, the continuous wavelet transforms (CWTs) of beam and vehicle displacements are
used to identify cracks which are modelled as rotational springs connecting elements. The moving sensor is found to be
more effective than the fixed sensor and small cracks with a depth of more than 10% of beam depth are detected. The
authors develop a damage index which has an explicit expression and can identify crack depth as well as location. In this paper, the aim is to investigate the effectiveness of wavelet based indirect approach for the monitoring of
bridges which uses vehicle accelerations. Firstly, in theoretical simulations, a simplified VBI simulation model is created
in MATLAB [21] and is used to investigate the effectiveness of the approach in detecting damage in a bridge. A
time-frequency analysis is carried out in order to identify the existence and/or location of two types of damage from the
vehicle accelerations. For this purpose, the accelerations are processed using a CWT. Bridge span length, vehicle speed,
road roughness and damage severity and/or location are varied in simulations to investigate the effect on the accuracy of
results. Secondly, in the laboratory, a scaled vehicle-bridge model is used which consists of a scaled two-axle vehicle and
a simply supported steel beam, which incorporates a scaled road surface profile. This experiment is carried out to validate
results of the theoretical analysis and investigate the effects of varying vehicle configuration and speed on the ability of
the approach to detect changes in the bridge response from the CWT of vehicle accelerations.
2. METHODOLOGY
2.1. Vehicle-Bridge Interaction Model
The VBI model used in theoretical simulations is a coupled system (Fig. 1) with the solution given at each time step using
the Wilson-Theta direct integration scheme. Similar models incorporating the coupling of the vehicle and bridge can be
found in the literature [22, 23] and González [24] has carried out reviews of these and other models.
The vehicle model is represented by a 2 degree of freedom half-car which crosses the bridge model at constant speed
c (Fig. 1). The two degrees of freedom of the model correspond to sprung mass bounce displacement, 𝑦𝑠, and sprung mass
pitch rotation, 𝜃𝑠. The vehicle body and axle component masses are represented by the sprung mass, 𝑚𝑠 = 18000 kg. A
combination of springs of linear stiffness 𝐾𝑖 = 1.42 × 106 N/m and viscous dampers with damping coefficient 𝐶𝑖 = 10 ×
103
N s/m represent the suspension components for the front and rear axles (𝑖 = 1, 2). Also, 𝐼𝑠 = 103840 kg m2
is the
sprung mass moment of inertia and the distance of each axle to the vehicle’s centre of gravity (o) is given by 𝐷𝑖 = 2.375 m.
(𝑖 = 1,2). The vehicle has both bounce and pitch frequencies of 2 Hz. The equations of motion of the vehicle are obtained
by imposing equilibrium of all forces and moments acting on the vehicle and expressing them in terms of the degrees of
freedom. Then, the vehicle system can be written for the purpose of coupling with the bridge model as:
𝐌𝐯�̈�𝐯 + 𝐂𝐯�̇�𝐯 + 𝐊𝐯𝐲𝐯 = 𝐟𝐯 (1)
where 𝐌𝐯, 𝐂𝐯, and 𝐊𝐯 are, respectively, the mass, damping and stiffness matrices of the vehicle while 𝐟𝐯 is the time
varying force vector applied to the vehicle and 𝐲𝐯 = {𝑦𝑠, 𝜃𝑠}T is its displacement vector. Sprung mass acceleration
measurements are recorded above the suspension of each axle in simulations (Fig. 1) and the relationship between the
degrees of freedom of the vehicle and the measurements is defined by the following equation:
�̈�𝑠,𝑖 = �̈�𝑠 − (−1)𝑖𝐷𝑖�̈�𝑠 ; 𝑖 = 1,2 (2)
The bridge is represented by a simply supported FE beam model (Fig. 1) of total span length L. It consists of discretised
beam elements with 4 degrees of freedom which have constant mass per unit length, µ, modulus of elasticity E and second
moment of area J. It follows that the beam element stiffness is the product of E and J, denoted EJ. The response of the
beam model to a series of moving time-varying forces is given by the system of equations:
𝐌𝐛�̈�𝐛 + 𝐂𝐛�̇�𝐛 + 𝐊𝐛𝐰𝐛 = 𝐍𝐛 𝐟𝐢𝐧𝐭 (3)
where 𝐌𝐛, 𝐂𝐛 and 𝐊𝐛 are (n × n) global mass, damping and stiffness matrices of the beam model respectively, 𝐰𝐛 , �̇�𝐛
and �̈�𝐛 are the (n × 1) global vectors of nodal bridge displacements and rotations, their velocities and accelerations
respectively, and 𝐍𝐛𝐟𝐢𝐧𝐭 is the (n × 1) global vector of forces applied to the bridge nodes. The location matrix 𝐍𝐛 consists
of zero entries and Hermitian shape function vectors, 𝑁𝑖. The parameter, n is the total number of degrees of freedom of the
bridge. Rayleigh damping is adopted here to model the damping of the experimental beam:
𝐂𝐛 = 𝐌𝐛 + 𝐊𝐛 (4)
where and are constants. The damping ratio ξ is assumed to be the same for the first two modes and and are
obtained from = 2 ξ12/(1+2) and = 2 ξ/(1+2) where 1 and 2 are the first two natural frequencies of the bridge
[25]. The properties of the three bridge spans used in simulations are given in Table 1.
The vehicle and bridge systems are coupled at the contact point of the wheel via the interaction force 𝐟𝐢𝐧𝐭. Eqs. (1) and (3)
are combined to form the coupled system of equations as:
𝐌𝐠�̈� + 𝐂𝐠�̇� + 𝐊𝐠𝐮 = 𝐟 (5)
where 𝐌𝐠 is the combined system mass matrix, 𝐂𝐠 and 𝐊𝐠 are coupled time-varying system damping and stiffness
matrices respectively and 𝐟 is the system force vector (see Appendix A). Also, 𝐮 = {𝐲𝐯, 𝐰𝐛}𝐓 is the displacement vector of
the system. Eq. (5) is solved using the Wilson-Theta integration scheme [26, 27] using the optimal value of the parameter
θ = 1.421 for unconditional stability [28].
Fig. 1 Vehicle-Bridge Interaction Model
Table 1 Finite element beam properties
Span Length,
L (m)
Intact Element
Stiffness, EJ (N m2)
Mass per unit
length, µ (kg/m)
Damping,
ξ (%)
1st natural frequency
of vibration, fb,1(Hz)
15 1.846 × 1010
28 125 3 5.66
25 4.865 × 1010
18 358 3 4.09
35 1.196 × 1011
21 752 3 3.01
2.2. Experimental Setup
The experimental setup is shown in Fig. 2(a). A scaled two–axle vehicle model (Fig. 2(b)) is fitted with 2 accelerometers
to monitor the vehicle bounce motion; these are located at the centre of the front and rear axles respectively. It also
includes a wireless router and data logger which allow the acceleration data to be recorded remotely. The vehicle model
can be adjusted to obtain different axle configurations and dynamic properties. The properties of the three vehicle model
configurations chosen for these experiments are given in Table 2. The axle spacing and track width for all models were 0.4
m and 0.2 m respectively. The speed of the vehicle was maintained constant by an electronic controller as it crossed the
bridge while its entry and exit to the beam was monitored using strain sensors. The scaled vehicle speeds adopted for the
experiment are S1 = 0.93 m/s and S2 = 1.63 m/s.
The scaled bridge model used in the experiment simply supported steel beam with span, Lexp, of 5.4 m (Fig. 2(c)) which
incorporates a scaled road surface profile. It is fitted with accelerometers and displacement transducers at quarter span,
mid-span and three-quarter span to measure its response during vehicle crossings. For the experiment, three damping
scenarios are investigated, named Intact, C and ABCDE. The Intact scenario represents the beam with no adjustments.
Scenarios C and ABCDE represent the beam with its damping adjusted; old displacement transducers are applied at
particular points on the beam in addition to a 17.8 kg mass added at midspan. The layout of these “dampers” is illustrated
in Fig. 2(a). The old transducers provide frictional resistance to bridge displacements at the chosen locations and hence
increase the damping. The additional mass adjusts the frequency of the beam as often damage which causes changes in
damping may cause some changes in frequency also. The beam properties are given in Table 3. A sampling frequency of
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